What is the difference between an isosceles and an equilateral trapezium

If you read this webpage, you see there are disagreements on definitions.
If your text material defines a trapezoid as a quadrilateral having exactly one pair of parallel sides then there are no equilaterals.
However, if it is defined as a quadrilateral with at least one pair of parallel sides, then being equilateral implies the figure is a rhombus which includes squares.
One the other hand, an isosceles trapezoid is one in which that is a pair of consecutive angles having the same measure.